From local Torelli to global Torelli
Algebraic Geometry
2016-09-06 v4
Abstract
We introduce the notions of strong local Torelli and T-class for polarized manifolds, and prove that strong local Torelli implies global Torelli theorem on the Torelli spaces for polarized manifolds in the T-class. We discuss many new examples of projective manifolds for which such global Torelli theorem holds. As applications we prove that, in these cases, a canonical completion of the Torelli space is a bounded pseudoconvex domain in complex Euclidean space, and show that generic Torelli implies global Torelli on moduli space with certain level structure.
Cite
@article{arxiv.1512.08384,
title = {From local Torelli to global Torelli},
author = {Kefeng Liu and Yang Shen},
journal= {arXiv preprint arXiv:1512.08384},
year = {2016}
}
Comments
Some clarifications are added and two simpler proofs of Theorem 5.9 are given. arXiv admin note: text overlap with arXiv:1205.4207, arXiv:1305.0231